ANTIDERIVATIVES OF TRIGONOMETRIC FUNCTIONS.pdf

EllenMaeNasayao 358 views 11 slides Sep 03, 2023
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basic cal


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ANTIDERIVATIVES
OF TRIGONOMETRIC
FUNCTIONS
ANTIDERIVATIVES
OF TRIGONOMETRIC
FUNCTIONS
BASIC CALCULUS
MS. ELLEN NASAYAO

TRIGONOMETRIC FUNCTIONS
Sine θ= opposite/hypotenuse
Cosine θ= adjacent/hypotenuse
Tangent θ= opposite/adjacent
Cosecantθ=hypotenuse/opposite
Secantθ =hypotenuse/adjacent
Cotangentθ =adjacent/opposite
TRIGONOMETRIC FUNCTIONS

TRIGONOMETRIC IDENTITIESTRIGONOMETRIC IDENTITIES

ANTIDERIVATIVES OF
TRIGONOMETRIC FUNCTIONS
ANTIDERIVATIVES OF
TRIGONOMETRIC FUNCTIONS

EXAMPLE 1
(���??????−�??????�??????)�??????
= ���??????�??????− �??????�??????�??????
=�??????�??????−(−���??????)+??????
=�??????�??????+���??????+??????

EXAMPLE 2
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2
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2
??????+1=���
2
??????
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2
??????=���
2
??????−1
= (���
2
??????−1)�??????
= ���
2
??????�??????− 1�??????
=−���??????−??????+??????

EXAMPLE 3
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2
??????�??????
�??????�
2
??????+1=���
2
??????
�??????�
2
??????=���
2
??????−1
= (���
2
??????−1)�??????
= ���
2
??????�??????− 1�??????
=�??????�??????−??????+??????

EXAMPLE 4

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2
??????
�??????
= (
�??????�??????
���??????���??????
)�??????
= (
1
���??????

�??????�??????
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)�??????
= (���??????∙�??????�??????)�??????
=���??????+??????

EXAMPLE 5
(8���??????+3�??????�??????)�??????
=8 ���??????+3 �??????�??????�??????
=8�??????�??????+3(−���??????)+??????
=8�??????�??????−3���??????+??????

EXAMPLE 6
(4���
2
??????−���??????�??????�??????)�??????
=4 ���
2
??????− (���??????�??????�??????)�??????
=4�??????�??????−���??????+??????

WHAT IF I-TRY NATIN???
1. 5���??????���??????�??????
2. 3���
2
??????�??????
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